Ryan, 36, completed 67% of his throws for 3,968 yards, 20 touchdowns and 12 interceptions last season. The four-time Pro Bowl selection is entering his 14th season.
Ryan completed 65% of his throws for 4,581 yards, 26 scores and 11 interceptions in 16 starts in 2020, when he led the league is passing attempts and completions.
The 2016 NFL MVP is the Falcons' franchise leader with 59,735 passing yards and 367 passing touchdowns.
The No. 3 overall pick in the 2008 NFL Draft is signed through 2023. He is due a $16.2 million base salary in 2022.
Ryan brings stability to the Colts' quarterback room just a week after the team traded 2021 starter Carson Wentz to the Washington Commanders. The Falcons now will need to find a starter at the position for the first time in more than a dozen years.
The Falcons have the No. 8 overall pick in the 2022 NFL Draft.